A known dual-battery system includes a starter battery and a vehicle electrical system battery, e.g., see: German Patent 40 28 242 A1. Arranged between the starter battery and the vehicle electrical system battery is a starter battery switch that is closed during a starting operation so that both batteries are connected to one another. Primary and secondary loads are then powered via both batteries. "Primary load" is understood to be loads essential for starting and driving capability or for vehicle safety, and "secondary load" to be for comfort components. In order to prevent any discharge of the starter battery, a control device senses the charge states of each of the starter battery and the vehicle electrical system battery. If the charge state of the starter battery drops below that of the vehicle electrical system battery, so that charging of the vehicle electrical system battery would take place at the expense of the starter battery, the control device will break the connection between the batteries by opening the starter battery switch. The known dual-battery system is disadvantageous firstly because the starter battery is on-load even after the starting operation has taken place, and secondly because the complexity of measuring and sensing the charge states of the two batteries is quite substantial.